LONDON — Tony Blair offered to unofficially advise Rebekah Brooks and News Corp. Chairman Rupert Murdoch at the height of the phone-hacking scandal in 2011 that led to the closure of the News of the World tabloid, prosecutors said.

Rebekah Brooks, then the head of News Corp.’s British unit, had an hour-long discussion with Blair, a former British prime minister, in which he also proposed an independent inquiry into allegations the newspaper accessed voice-mail messages of celebrities, politicians and murder victims, according to an email disclosed at a criminal trial in London, Wednesday.

Brooks, 45, sent the email describing the conversation to Murdoch’s son James, then the New York-based company’s deputy chief operating officer on July 11, 2011, the day after the final issue of the News of the World was published. The scandal deepened a week earlier after the discovery that News Corp. journalists had hacked the phone of a murdered school girl.

Blair offered his services as an unofficial adviser to the Murdochs and Brooks, but the offer “needs to be between us,” Brooks told James Murdoch in the email. Brooks was arrested six days later.

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Brooks is one of seven people on trial for charges related to phone hacking, bribery of public officials and hiding evidence. Andy Coulson, another former editor of the weekly tabloid and who later advised current Prime Minister David Cameron, is also on trial in the case.

Blair also told Brooks to keep a clear head and “tough up,” according to her email.

“Keep strong and definitely sleeping pills,” Blair said, according to the e-mail submitted by prosecutors. “Need to have clear heads and remember no rash short term solutions as they only give you long term headaches.”

An earlier email between the two discussed sales of the final issue of the News of the World.

Brooks mentioned a “Hutton-style” investigation, referring to a judicial review related to the Iraq war.

“This was Mr. Blair simply giving informal advice over the phone,” Blair’s office said in an emailed statement. “Though he knew nothing personally about the facts of the case, in a situation as serious as this it was essential to have a fully transparent and independent process to get to the bottom of what had happened.”

Days before the tabloid was scheduled to close, Brooks sent an email to James Murdoch on July 8, prosecutors said. The note, titled “Plan B,” outlined her plans to distance herself from the growing scandal and lay blame on other company officials, including Les Hinton, the then-CEO of News Corp.’s Dow Jones unit, and Colin Myler, the then editor of the News of the World.

The “result of a report when published would slam Les, Colin, etc and vindicate my position (or not),” she said in the email. She suggested an internal announcement be leaked to the media.

“Our internal investigations were woeful and limited and we failed to hold the right people accountable,” Brooks said in a draft of the announcement she sent to James Murdoch. She said “it will be written as a slippery slope for me but I hardly have any reputation left.”

The prosecution has now officially closed its case in the trial that has lasted almost four months and seen film stars, politicians and celebrities testify. Brooks’s lawyers will begin their defense tomorrow.

Other defendants in the case include Stuart Kuttner, the former managing editor of the News of the World, who is accused of phone hacking. The newspaper’s one-time royal reporter, Clive Goodman, is charged with conspiring to commit misconduct in a public office.

Brooks’ husband, Charlie, her former assistant Cheryl Carter, and the British unit’s former head of security, Mark Hanna, face charges of conspiring to pervert the course of justice. All seven have pleaded not guilty.